Solve for $x$ and $y$ using elimination. ${-6x+6y = 6}$ ${5x+5y = 15}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x+30y = 30}$ $30x+30y = 90$ Add the top and bottom equations together. $60y = 120$ $\dfrac{60y}{{60}} = \dfrac{120}{{60}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-6x+6y = 6}\thinspace$ to find $x$ ${-6x + 6}{(2)}{= 6}$ $-6x+12 = 6$ $-6x+12{-12} = 6{-12}$ $-6x = -6$ $\dfrac{-6x}{{-6}} = \dfrac{-6}{{-6}}$ ${x = 1}$ You can also plug ${y = 2}$ into $\thinspace {5x+5y = 15}\thinspace$ and get the same answer for $x$ : ${5x + 5}{(2)}{= 15}$ ${x = 1}$